Section 14.4: Climatic Applications oE SSA
273
of the above two oscillations shows in fact that these two oscillations are
phase-Iocked. That is, the 35-day oscillation is in fact a harmonie of the
70-day oscillation. This has important dynamical consequences since the two
phenomena cannot be studied separately. This also emphasizes the non linear
nature of these oscillations. Indeed, should the underlying dynamical system
be linear, the solutions would result in two periodic orbits that would be
symmetrie and ellipsoidal in phase-space, whereas here they are more likely
to result in one periodic orbit of period 70 days distorted in such a way that
it generates a nonvanishing harmonie.
The time-Iocal nature of MSSA allows one also to distinguish periods of
high amplitude, called oscillation speils. Such is the case, for instance, du ring
winters 61-62 and 77-78, for the 70-day oscillation. ST-EOFs 7 and 8 gathered explain globally about 3% of the total variance (annual cycle removed).
However, the ratio of the sum of squares of the two ST-PCs involved to the
total sum of squares of all ST-PCs represent the explained local variance (in
time), and can be as high as 20% during high-amplitude spells. Thus, MSSA
allows the quantification of the variance explained in the time domain, and
to extract high-amplitude speIls.
In order to illustrate the fact that high-amplitude spells result in important
changes in the ßow circulation, Figure 14.4 shows the composite average ofthe
700 hPa heights over days selected in (i) the 20 highest-amplitude spells of the
70 day oscillation, and (ii) found simultaneously in particular phases of the
two oscillations. This composite is particularly interesting since it exhibits
a pronounced European blocking structure. Thus, one possible origin of
blocking may simply be the interference pattern of two oscillating phenomena,
which would contradict the strongly nonlinear character of blocking. In fact,
this interference situation cannot explain blocking in general, since only a
small fraction of blocking events turn out to be present in the composite of
Figure 14.4.
A more systematical study of the correlation between weather regimes
(Molteni et al. , 1990; Vautard, 1990; Cheng and Wall ace , 1993; Kimoto
and Ghil; 1993), such as blocking, and these low-frequency oscillations would
show that the occurrence of the former is inßuenced by the phase of the latter
(Plaut and Vautard, 1994). In other words, one can think ofthe oscillations as
creating favorable environments for the onset of particular weather regimes.
Such a phenomenon can also be observed with the environment created by
EI Niiio on the mid-Iatitude ßow (see Chapter 6).
This last point has important consequences for climate modeling and longrange forecasting. First, it implies that a good climate model must simulate
correctly the intraseasonal oscillations in order to simulate also correctly the
weather regimes. Second, the occurrence of weather regimes is not random,
since they are inßuenced by these oscillations. As the oscillations are intrinsically predictable phenomena, they are a source of long-range predictability
in the mid-Iatitudes. We shall test this idea now by constructing an empirical
model based on MSSA predictors.
273
of the above two oscillations shows in fact that these two oscillations are
phase-Iocked. That is, the 35-day oscillation is in fact a harmonie of the
70-day oscillation. This has important dynamical consequences since the two
phenomena cannot be studied separately. This also emphasizes the non linear
nature of these oscillations. Indeed, should the underlying dynamical system
be linear, the solutions would result in two periodic orbits that would be
symmetrie and ellipsoidal in phase-space, whereas here they are more likely
to result in one periodic orbit of period 70 days distorted in such a way that
it generates a nonvanishing harmonie.
The time-Iocal nature of MSSA allows one also to distinguish periods of
high amplitude, called oscillation speils. Such is the case, for instance, du ring
winters 61-62 and 77-78, for the 70-day oscillation. ST-EOFs 7 and 8 gathered explain globally about 3% of the total variance (annual cycle removed).
However, the ratio of the sum of squares of the two ST-PCs involved to the
total sum of squares of all ST-PCs represent the explained local variance (in
time), and can be as high as 20% during high-amplitude spells. Thus, MSSA
allows the quantification of the variance explained in the time domain, and
to extract high-amplitude speIls.
In order to illustrate the fact that high-amplitude spells result in important
changes in the ßow circulation, Figure 14.4 shows the composite average ofthe
700 hPa heights over days selected in (i) the 20 highest-amplitude spells of the
70 day oscillation, and (ii) found simultaneously in particular phases of the
two oscillations. This composite is particularly interesting since it exhibits
a pronounced European blocking structure. Thus, one possible origin of
blocking may simply be the interference pattern of two oscillating phenomena,
which would contradict the strongly nonlinear character of blocking. In fact,
this interference situation cannot explain blocking in general, since only a
small fraction of blocking events turn out to be present in the composite of
Figure 14.4.
A more systematical study of the correlation between weather regimes
(Molteni et al. , 1990; Vautard, 1990; Cheng and Wall ace , 1993; Kimoto
and Ghil; 1993), such as blocking, and these low-frequency oscillations would
show that the occurrence of the former is inßuenced by the phase of the latter
(Plaut and Vautard, 1994). In other words, one can think ofthe oscillations as
creating favorable environments for the onset of particular weather regimes.
Such a phenomenon can also be observed with the environment created by
EI Niiio on the mid-Iatitude ßow (see Chapter 6).
This last point has important consequences for climate modeling and longrange forecasting. First, it implies that a good climate model must simulate
correctly the intraseasonal oscillations in order to simulate also correctly the
weather regimes. Second, the occurrence of weather regimes is not random,
since they are inßuenced by these oscillations. As the oscillations are intrinsically predictable phenomena, they are a source of long-range predictability
in the mid-Iatitudes. We shall test this idea now by constructing an empirical
model based on MSSA predictors.